Datasets:
Formats:
json
Languages:
English
Size:
1K - 10K
Tags:
matter-embryogenesis
developmental-fabrication
nanotechnology
self-assembly
materials-science
passive-networks
File size: 5,484 Bytes
52fc221 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 | from pathlib import Path
import json
import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from matplotlib.collections import LineCollection
from recovery import joint_value
ROOT=Path(__file__).resolve().parents[1]
plt.rcParams.update({'font.family':'DejaVu Sans','font.size':10,
'axes.spines.top':False,'axes.spines.right':False})
C={'contract':'#167f89','conventional_joint':'#65a6aa','open_loop':'#919aa6',
'blueprint':'#5d748a','blind_reserve':'#c4a06a','sensor_only':'#9b7eaa',
'early_seal':'#bd736b','biased_reference':'#dd9b59'}
def main():
out=ROOT/'figures';out.mkdir(exist_ok=True)
summary=json.loads((ROOT/'results/summary.json').read_text())
fig,axs=plt.subplots(1,2,figsize=(10,4.5),layout='constrained',sharey=True)
names=summary['methods']
labels=['Open loop','Blueprint repair','Blind reserve','Sensors only','Early seal',
'Response contracts','Conventional joint','Biased reference']
for ax,dim in zip(axs,[2,3]):
rows=[x for x in summary['summaries'] if x['dimension']==dim]
for i,row in enumerate(rows):
ax.barh(i,row['functional_yield_count']/row['replicates'],color=C[row['method']])
ax.text(min(.98,row['functional_yield_count']/row['replicates']+.025),i,
f"{row['functional_yield_count']}/{row['replicates']}",ha='right' if row['functional_yield_count']==32 else 'left',va='center',
color='white' if row['functional_yield_count']==32 else '#26364a',fontsize=9)
ax.set(xlim=(0,1.12),xlabel='Completed functional yield',title=f'{dim}-D passive network')
ax.set_yticks(range(len(labels)),labels);ax.grid(axis='x',alpha=.18)
axs[0].invert_yaxis()
fig.savefig(out/'functional_yield.png',dpi=200);plt.close(fig)
checks=json.loads((ROOT/'results/theorem_checks.json').read_text())
xy=checks['composition_examples']
fig,axs=plt.subplots(1,2,figsize=(10,4.1),layout='constrained')
ax=axs[0]
ax.scatter([x['largest_local_error'] for x in xy],[x['global_error'] for x in xy],s=12,c=[x['modules'] for x in xy],cmap='viridis',alpha=.6)
ax.plot([0,.10],[0,.10],color='#b75850',lw=1.4,label='Proved upper envelope')
ax.set(xlabel='Largest local relative error',ylabel='Global relative error',title='300 multiport composition checks',xlim=(0,.10),ylim=(0,.10));ax.legend(fontsize=8)
ax=axs[1]
bounds=np.array(checks['weighted_examples']);order=np.argsort(bounds[:,1])
ax.fill_between(np.arange(len(order)),bounds[order,0],bounds[order,2],color='#167f89',alpha=.2,label='Deterministic energy bounds')
ax.plot(bounds[order,1],color='#203044',lw=1.3,label='Solved network response')
ax.set(xlabel='Random instance, sorted by response',ylabel='Conductance / target',title='250 positive-conductance checks');ax.legend(fontsize=8)
fig.savefig(out/'response_certificates.png',dpi=200);plt.close(fig)
fig,axs=plt.subplots(1,3,figsize=(10,3.5),layout='constrained')
for ax,meth,title in zip(axs,['open_loop','early_seal','contract'],['Open loop','Early seal','Response contracts']):
d=np.load(ROOT/'results'/f'2d_{meth}.npz')
x=d['coordinates'];segs=x[d['edges']]
color=np.abs(d['final']/d['target']-1)
lc=LineCollection(segs,array=color,cmap='magma_r',norm=plt.Normalize(0,.6),linewidths=3)
ax.add_collection(lc);ax.scatter(x[:,0],x[:,1],s=8,c=np.where(d['sealed'],'#203044','#e29c3d'))
ax.set(xlim=(-.4,7.4),ylim=(-.4,7.4),aspect='equal',title=title);ax.set_xticks([]);ax.set_yticks([])
fig.colorbar(lc,ax=axs,shrink=.75,label='Local relative response error')
fig.savefig(out/'network_snapshots.png',dpi=200);plt.close(fig)
fig,axs=plt.subplots(1,2,figsize=(10,4),layout='constrained')
s=np.linspace(0,4,251);S,T=np.meshgrid(s,s)
value=joint_value(S,T,12)
im=axs[0].pcolormesh(S,T,value,cmap='RdBu',vmin=-4,vmax=4,shading='auto')
axs[0].contour(S,T,value,levels=[0],colors=['black'],linewidths=1)
axs[0].set(xlabel='Normalized diagnostic precision',ylabel='Normalized repair mobility',title='Matched service reserve (inherited EDD law)')
fig.colorbar(im,ax=axs[0],label='Net reserve value')
xs=np.linspace(0,1,301)
for k in [0,.1,1,10]:
axs[1].plot(xs,(k/(1+k))*xs,label=f'Control strength {k:g}')
axs[1].set(xlabel='Fraction of error made observable',ylabel='Fraction of quadratic loss recoverable',title='Neither resource substitutes for the other');axs[1].legend(fontsize=8)
fig.savefig(out/'matched_recovery.png',dpi=200);plt.close(fig)
fig,axs=plt.subplots(1,2,figsize=(10,3.8),layout='constrained')
L=np.logspace(-7,-2,250)
for D,label in [(1e-9,'Small solute, D = 10⁻⁹ m²/s'),(1e-11,'Slow complex, D = 10⁻¹¹ m²/s')]:
axs[0].loglog(L,L*L/D,label=label)
axs[0].set(xlabel='Diffusion length (m)',ylabel='L² / D (s)',title='Diffusion time; no reaction included');axs[0].legend(fontsize=8)
R=np.logspace(1,12,240);delta=.01
for a in [.2,.6,.9]:
H=np.ceil(np.log(R/delta)/-np.log1p(-a))
axs[1].semilogx(R,H,label=f'Conditional acceptance a = {a}')
axs[1].set(xlabel='Number of repairable modules',ylabel='Sufficient retry rounds',title='Logical rounds, excluding transport time');axs[1].legend(fontsize=8)
for ax in axs:ax.grid(alpha=.18)
fig.savefig(out/'scaling_limits.png',dpi=200);plt.close(fig)
if __name__=='__main__':main()
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